Question

A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is $44m$, find the cost of painting it, given the cost of painting is $Rs2$ per $100c{m}^2$.

• A. $Rs.62,600$
• B. $Rs.63,000$
• C. $Rs.61,000$
• D. $Rs.61,600$

Answer 1

The correct option is D $Rs.61,600$

The base of the dome is circular.
Let the radius of the dome be r.
Given, circumference of the dome $=44m$
$\Rightarrow 2\times \frac{22}{7}\times r=44$
$\Rightarrow r=7m$
Curved Surface Area of a hemisphere of radius ${}^{\prime }{r}^{\prime }=2\pi r^2$
So, CSA of the dome $=2\times \frac{22}{7}\times 7^2$

$=308sqm$

$=3080000sqcm$
Cost of painting the dome at Rs$2per100{cm}^2=\frac{3080000}{100}\times 2$ = Rs 61,600